High-speed serial link channels delivering an effective data rate above 5 Gb/s in a backplane environment are subject to significant signal distortion due to inter-symbol interference (ISI). Transmitters and receivers need to compensate for most of the signal distortion using very low complexity schemes in order to obtain a target bit error rate (BER) of less than or equal to 10−17 at Gb/s rates and under severe power and complexity restrictions. This constrained space presents significant challenges to well-known signal processing and coding techniques, and sub-optimal but efficient alternatives are sometimes needed to fulfill the task.
Attenuation caused by conductor and dielectric losses causes dispersion ISI. Another important ISI component is reflections, which are essentially multipath components of a signal and originate from impedance discontinuities such as those caused by connectors of line cards at both transmit and receive ends. In addition to ISI distortion, cross-talk effects from far and near end adjacent channels is becoming increasingly significant.
To counteract channel attenuation at high bit rates, conventional 2-level pulse amplitude modulation (2-PAM) signaling may be replaced by other multi-level signaling schemes that utilize more than two signal levels. That is, in a 2-PAM signaling system, each conductor in the system may carry signals at one of two signal levels (i.e., at either a logic zero level or a logic one level). Thus, in a 2-PAM signaling system, each conductor in the system can only transmit one bit of data at a time. However, in a 4-level pulse amplitude modulation (4-PAM) signaling system, for example, each conductor in the system may carry signals at four different signal levels (i.e., four different symbols). Thus, in a 4-PAM signaling system, each conductor in the system can transmit two bits of data simultaneously at one half the symbol rate for an equivalent bandwidth.
While advantageous in channels with dominant attenuation, signaling systems that utilize more than two signal levels are more sensitive to reflections and cross-talk than 2-PAM signaling systems due to the reduction in signal margin as a result of carrying more information per symbol. Thus, in cases where high loss and reflections are combined, the advantages of signaling systems that utilize more than two signal levels over 2-PAM signaling systems may be lost.
In order to preserve the advantages of signaling systems that utilize more than two signal levels over 2-PAM signaling systems, transition-limiting codes have been developed which reduce or eliminate the number of full-swing transitions (FST) between sequential symbols in a multi-level signaling system. Reducing or eliminating the number of FST between sequential symbols enhances system performance in terms of: 1.) voltage margins (Vm), by reducing peak distortion (PD) via the elimination of one or more worst case sequences; and 2.) timing margins (Tm), especially at outer eyes where FST close eyes the most.
These same transition-limiting codes have also been developed to secure a minimum density of desirable symbol transitions useful for clock recovery. These clock data recovery (CDR) transitions prevent continuous phase drifting from an optimum sampling point at the center of an eye in plesiochronous systems with frequency offsets between received data and a local receive clock.
A problem sometimes arises when determining which of these transition-limiting codes may be best suited for use in a particular multi-level signaling system. Accordingly, it would be desirable to provide a technique for determining an optimal transition-limiting code for use in a multi-level signaling system.